diff --git a/Doc/library/smtpd.rst b/Doc/library/smtpd.rst
index d84e74a8cea..803430f1bde 100644
--- a/Doc/library/smtpd.rst
+++ b/Doc/library/smtpd.rst
@@ -13,11 +13,10 @@
 
 This module offers several classes to implement SMTP (email) servers.
 
-.. seealso::
-
-    The `aiosmtpd <http://aiosmtpd.readthedocs.io/>`_ package is a recommended
-    replacement for this module.  It is based on :mod:`asyncio` and provides a
-    more straightforward API.  :mod:`smtpd` should be considered deprecated.
+.. deprecated:: 3.6
+   The `aiosmtpd <https://aiosmtpd.readthedocs.io/>`_ package is a recommended
+   replacement for this module.  It is based on :mod:`asyncio` and provides a
+   more straightforward API.
 
 Several server implementations are present; one is a generic
 do-nothing implementation, which can be overridden, while the other two offer
diff --git a/Doc/whatsnew/3.10.rst b/Doc/whatsnew/3.10.rst
index 987d125a011..6b6578b4097 100644
--- a/Doc/whatsnew/3.10.rst
+++ b/Doc/whatsnew/3.10.rst
@@ -883,6 +883,12 @@ The :meth:`~array.array.index` method of :class:`array.array` now has
 optional *start* and *stop* parameters.
 (Contributed by Anders Lorentsen and Zackery Spytz in :issue:`31956`.)
 
+asynchat, asyncore, smtpd
+-------------------------
+These modules have been marked as deprecated in their module documentation
+since Python 3.6.  An import-time :class:`DeprecationWarning` has now been
+added to all three of these modules.
+
 base64
 ------
 
diff --git a/Lib/asynchat.py b/Lib/asynchat.py
index f4ba361bd4a..de26ffa648f 100644
--- a/Lib/asynchat.py
+++ b/Lib/asynchat.py
@@ -48,6 +48,14 @@
 import asyncore
 from collections import deque
 
+from warnings import warn
+warn(
+    'The asynchat module is deprecated. '
+    'The recommended replacement is asyncio',
+    DeprecationWarning,
+    stacklevel=2)
+
+
 
 class async_chat(asyncore.dispatcher):
     """This is an abstract class.  You must derive from this class, and add
diff --git a/Lib/asyncore.py b/Lib/asyncore.py
index eeea4888861..b1eea4bf652 100644
--- a/Lib/asyncore.py
+++ b/Lib/asyncore.py
@@ -57,6 +57,13 @@
      ENOTCONN, ESHUTDOWN, EISCONN, EBADF, ECONNABORTED, EPIPE, EAGAIN, \
      errorcode
 
+warnings.warn(
+    'The asyncore module is deprecated. '
+    'The recommended replacement is asyncio',
+    DeprecationWarning,
+    stacklevel=2)
+
+
 _DISCONNECTED = frozenset({ECONNRESET, ENOTCONN, ESHUTDOWN, ECONNABORTED, EPIPE,
                            EBADF})
 
diff --git a/Lib/smtpd.py b/Lib/smtpd.py
index 1e2adc87a2b..bc433312510 100755
--- a/Lib/smtpd.py
+++ b/Lib/smtpd.py
@@ -83,8 +83,6 @@
 import getopt
 import time
 import socket
-import asyncore
-import asynchat
 import collections
 from warnings import warn
 from email._header_value_parser import get_addr_spec, get_angle_addr
@@ -94,6 +92,19 @@
     "MailmanProxy",
 ]
 
+warn(
+    'The smtpd module is deprecated and unmaintained.  Please see aiosmtpd '
+    '(https://aiosmtpd.readthedocs.io/) for the recommended replacement.',
+    DeprecationWarning,
+    stacklevel=2)
+
+
+# These are imported after the above warning so that users get the correct
+# deprecation warning.
+import asyncore
+import asynchat
+
+
 program = sys.argv[0]
 __version__ = 'Python SMTP proxy version 0.3'
 
diff --git a/Lib/test/test_support.py b/Lib/test/test_support.py
index 55d78b73335..b1d3411a865 100644
--- a/Lib/test/test_support.py
+++ b/Lib/test/test_support.py
@@ -292,8 +292,8 @@ def test_check_syntax_error(self):
 
     def test_CleanImport(self):
         import importlib
-        with import_helper.CleanImport("asyncore"):
-            importlib.import_module("asyncore")
+        with import_helper.CleanImport("pprint"):
+            importlib.import_module("pprint")
 
     def test_DirsOnSysPath(self):
         with import_helper.DirsOnSysPath('foo', 'bar'):